[AUTHOURITY NEED]is 'd cosx' available? (1 Viewer)

[ne plus ultra]

when i did intergration questions, i did it like this, for example:

intergral tanx dx
('intergral' here means the symbol...the big 's' like symbol....i dont know how to type in....||||- -)

then this is what i did:

intergral tanx dx
=intergral sinx dx/cosx
=intergral - d cosx/cosx
= - ln cosx + C
done.


my teacher says she never met anything like 'd cosx' here, so that i can't use it in doing the questions. instead we have to strictly follow the differenciate step which is:
dy=sinx dx
therefore dy/dx=sinx
therefore y=-cosx

however in my opinion, the only different between what i did and what the teacher said, is that she sub a 'y' as a medium in doing the question while i didnt. anyway both of us got the correct answer.
my teacher told me i must lose marks in HSC and i d better never use that again. i dont know how come mine is incorrect in the exam. isnt our purpose to solve the questions but not the from we write? i have use such a method for more than one year and nobody tell me it is not right...suddenly force me to change my brian make me extraodinarily uncomfortable.......- -
i need somebody who KNEW the HSC VERY MUCH to tell me if i can do 'd cosx' things in the exam.

(sorry for my messy english....><)

THANK YOU SOOO MUCH.......

 

[pLuvia]

I've never seen that d cosx before either, unless you meant d/dx(cosx). Because d(cosx) doesn't tell to what variable you are differentiating to, i.e d/dx(cosx) means to differentiate cosx in respect of x

The way I would do it, to show working would be
int.(tanx)dx
Let u=cosx
du=-sinxdx
Hence int.(tanx)dx=-ln(cosx)+C

 

[SeDaTeD]

I've done it plenty of times and received full marks. They're differentials. Plus, it makes integration by parts so much quicker and concise.

 

[kony]

yes it is allowed.

for example, integral sec²xtanxdx = integral tanxd(tanx) = (tan²x)/2

doing this is similar to a subsitution:

for integral sec²xtanxdx, let u = tanx
du=sec²xdx
therefore, integral udu = u²/2 = (tan²x)/2

as you can see, the answers are the same. as the above poster said, this is using a differential, where the variable being integrated against is changed to something other than x.

 

[ne plus ultra]

the method from #2 is how my teacher did. i m trying to do it in this way....- -|||| thank you~

i m so happy that upstairs two supporting me...^^ well are you guys sure about it s allowed in HSC not only in your school? then i ll show my teacher this thread and ask again....thank you guys so much.

any teacher here?

 

[buchanan]

It's OK if it's indefinite.

For definite ones however it's better to leave the limits as values of x and not change them to the corresponding values for what you end up integrating with respect to - unlike in substitution where you do change these values. The reason for this is that your answer is still going to be in terms of x before substituting values. For example: